M. YETTOU Mourad

MCA

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Department

Mathematics Department

Research Interests

Specialized in Mathematics Department. Focused on academic and scientific development.

Contact Info

University of M'Sila, Algeria

Email : mourad.yettou@univ-msila.dz

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Recent Publications

2024-09-18

Algebraic Integrations on Lattices

In this paper, we present the notion of integration with respect to a given derivation on a lattice. To that
end, we give the definitions of integrable elements of a lattice and their integral sets. We investigate several
characterizations and properties of integrations on a lattice.
Citation

M. YETTOU Mourad, (2024-09-18), "Algebraic Integrations on Lattices", [international] The 4th International Conference On Applied Algebra ICAA’2024 , Barika Center University

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2023-11-08

Associated functions of algebraic derivations on lattices

In this paper, associated functions of algebraic derivations on a lattice are defined. Some their characterizations and properties are provided. Moreover, relationships between derivations and those associated functions are established.
Citation

M. YETTOU Mourad, (2023-11-08), "Associated functions of algebraic derivations on lattices", [international] the first Sharjah International Conference on Mathematical Sciences , University of Sharjah, United Arab Emirates.

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2023-06-22

On homoderivations of lattices and their properties

In this paper, we would like to present our introduced notion of homoderivations on lattices which is a combination between meetmorphisms and derivations. To that end, we give some characterizations and properties of them. We investigate the relationship between derivations and homoderivations. Moreover, we study an interesting class of isotone homoderivations on a given lattice.
Citation

M. YETTOU Mourad, (2023-06-22), "On homoderivations of lattices and their properties", [national] The 1st National Conference on Applied Algebra , Barika Center University

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2023-01-15

INTEGRATIONS ON LATTICES

In this paper, we introduce the notion of integration with respect to a given derivation
on a lattice. More precisely, we give the definitions of integrable elements of a lattice and their
integral sets. We investigate several characterizations and properties of integrations on a lattice.
Also, we give a lattice structure to the family of integral sets with respect to a given integration.
Further, we provide a representation theorem for the lattice of fixed points of an isotone derivation
based on the family of integral sets. As an application of this notion of integration, we use the
integrable elements of a Boolean lattice to determine the necessary and sufficient conditions
under which a linear differential equation on this Boolean lattice has a solution
Citation

M. YETTOU Mourad, (2023-01-15), "INTEGRATIONS ON LATTICES", [national] Miskolc Mathematical Notes , Miskolc Mathematical Notes

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2022-09-01

HOMODERIVATIONS ON A LATTICE

In this paper, the concept of homoderivation on a lattice as a combination of two concepts of meet-homomorphisms and derivations is introduced. Some
characterizations and properties of homoderivations are provided. The relationship between derivations and homoderivations on a lattice is established. Also, an interesting class of homoderivations namely isotone homoderivations is studied. A characterization of the isotone homoderivations in terms of the meet-homomorphisms is given. Furthermore, a sufficient condition for a homoderivation to become isotonic is established.
Citation

M. YETTOU Mourad, (2022-09-01), "HOMODERIVATIONS ON A LATTICE", [national] Jordan Journal of Mathematics and Statistics , Jordan Journal of Mathematics and Statistics

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2022-06-15

(F, G)-DERIVATIONS ON A LATTICE

In the present paper, we introduce the notion of (F, G)-derivation on
a lattice as a generalization of the notion of (∧, ∨)-derivation. This newly notion
is based on two arbitrary binary operations F and G instead of the meet (∧) and
the join (∨) operations. Also, we investigate properties of (F, G)-derivation on a
lattice in details. Furthermore, we define and study the notion of principal (F, G)-
derivations as a particular class of (F, G)-derivations. As applications, we provide
two representations of a given lattice in terms of its principal (F, G)-derivations
Citation

M. YETTOU Mourad, (2022-06-15), "(F, G)-DERIVATIONS ON A LATTICE", [national] Kragujevac Journal of Mathematics , Kragujevac Journal of Mathematics

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2020-06-10

doctoral thesis: (F,G)-derivations on lattices

In this thesis, we have generalized the notion of (∧,∨)-derivation to (, )-
derivation on lattices, and investigated its properties in details. This
generalization is based on two arbitrary binary operations  and instead of the
lattice meet (∧) and join (∨) operations. To that end, a lot of preparatory work
were required. In particular, several properties of binary operations on an
arbitrary lattice were investigated, and two representation theorems of a lattice
based on a binary operation were provided. As specific notion of derivations on
lattices, we have studied the isotone and principal -derivations on a lattice, and
investigated their properties. We have ended this part by studying the lattice
structure of isotone -derivations on a lattice, and the ideal structures of the sets
of their -fixed points.
Citation

M. YETTOU Mourad, (2020-06-10), "doctoral thesis: (F,G)-derivations on lattices", [national] University of M’sila-Algeria

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2019-12-19

Isotone f-derivations on a lattice and their f-fixed points

In this work, we present the newly notion of f-derivations on a lattice and investigate their most
important properties. More precisely, we pay particular attention to study the ideal structure of
the set of f-fixed points of isotone f-derivations on a given lattice. As applications, we provide a
characterization of principal ideals and a representation of a lattice in terms of principal f-derivations.
Also, we give a representation of a distributive lattice based on f-fixed points of its isotone fderivations.
Citation

M. YETTOU Mourad, (2019-12-19), "Isotone f-derivations on a lattice and their f-fixed points", [international] The International Conference on Advances in Applied Mathematics , Tunisia

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2019-06-01

A BINARY OPERATION-BASED REPRESENTATION OF A LATTICE

In this paper, we study and characterize some properties of a given binary operation ona lattice. More specifically, we show necessary and sufficient conditions under which a binary
operation on a lattice coincides with its meet (resp. its join) operation. Importantly, we construct two new posets based on a given binary operation on a lattice and investigate some cases
that these two posets have a lattice structure. Moreover, we provide some representations of a given lattice based on these new constructed lattices.
Citation

M. YETTOU Mourad, (2019-06-01), "A BINARY OPERATION-BASED REPRESENTATION OF A LATTICE", [national] K Y B E R N E T I K A , K Y B E R N E T I K A

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2019-01-15

f-FIXED POINTS OF ISOTONE f-DERIVATIONS ON A LATTICE

In a recent paper, C¸ even and Ozt¨urk have generalized the notion of f-derivation on a lattice to f-derivation, where f is a given function of that
lattice into itself. Under some conditions, they have characterized the distributive and modular lattices in terms of their isotone f-derivations. In this
paper, we investigate the most important properties of isotone f-derivationson a lattice, paying particular attention to the lattice (resp. ideal) structures
of isotone f-derivations and the sets of their f-fixed points. As applications,we provide characterizations of distributive lattices and principal ideals of a
lattice in terms of principal f-derivations.
Citation

M. YETTOU Mourad, (2019-01-15), "f-FIXED POINTS OF ISOTONE f-DERIVATIONS ON A LATTICE", [national] Discussiones Mathematicae General Algebra and Applications , Discussiones Mathematicae General Algebra and Applications

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2018-12-18

Principal f-derivations on a lattice and their f-fixed points

In this work, we investigate the most important properties of
principal f-derivations on a lattice. More precisely, we pay particular attention to the lattice (resp. ideal) structures of principal f-derivations and the
sets of their f-fixed points. As applications, we provide a characterization
of principal ideals, and a representation of a lattice in terms of principal
f-derivations.
Citation

M. YETTOU Mourad, (2018-12-18), "Principal f-derivations on a lattice and their f-fixed points", [national] The National Workshops of Pure and Applied Mathematics , M’sila University

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